Phase-Based Gain-Modulation
(PBGM) control is realized by modulating controller gains in response to
the phase of the system state or tracking error. PBGM controllers have been
applied to robotic hands, parallel manipulators and flexible mechanisms
to give increased damping, reduced tracking error and friction compensation.

A novel method is presented
to establish Lyapunov stability for PBGM control. Prior PBGM stability results
incorporated a constraint which limited the range of provably stable systems.
The present result removes this constraint, establishing Lyapunov stability
for a substantially broader class of systems. Additionally, the new approach
decouples the selection of the Lyapunov function from the controller design,
permitting the controls designer to independently specify a switch function
which determines the application of gain modulation.

The present results are applied
to analyze PBGM control of the Sarcos dextrous manipulator, illuminating
the stability properties of control experiments previously reported in the
literature. Numerical methods for design calculations are also presented.